Proportional Relationships & k

What makes a relationship proportional?

Two quantities are proportional when their ratio is always the same. On a graph, that means a straight line through the origin (0, 0).

A ratio compares two quantities with the same units. Order matters: a ratio of cats to dogs is not the same as dogs to cats unless the problem says they are equivalent.

Write ratios in three ways: with a colon (3:4), as a phrase (3 to 4), or as a fraction (3/4) when it fits the context.

Finding the constant of proportionality

When you study finding the constant of proportionality, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

1. 1Pick any pair of values (x, y) from a table or graph.
2. 2Divide: k = y ÷ x.
3. 3Write the equation y = kx.

Why this matters

Proportional Relationships & k shows up constantly in spot proportional relationships and find the constant of proportionality. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

Key ideas from this lesson

1. What makes a relationship proportional?
2. Finding the constant of proportionality
3. Pick any pair of values (x, y) from a table or graph.
4. Divide: k = y ÷ x.
5. Write the equation y = kx.